Answer
$x=3.5$
$y=1.5$
$z=0.75$
Work Step by Step
We will denote price of a gallon of milk by $x$, price of bottle of water by $y$ and price of snack-size bag of chips by $z$.
We are given the system:
$\begin{cases}
x+7y+4z=17\\
y=2z\\
x=y+2
\end{cases}$
We substitute $y$ in places of $2z$ in the first equation. substract $y$ from both sides in the second equation to get the variables on one side of the equation.
$\begin{cases}
x+7y+2(2z)=x+7y+2y=xx+9y=17\\
x-y=y-y+2=x-y=2
\end{cases}$
We will use the addition method. Multiply the Equation 2 by $9$ and add it to Equation 1.
$\begin{cases}
x+9y=17\\
9x-9y=18
\end{cases}$
$10x=35$
$x=3.5$
Substitute the value of $x$ in the Equation $x=y+2$ to determine $y$:
$3.5=y+2$
$1.5=y$
Substitute the values of $x, y$ in Equation 1 of the given system to find $z$:
$x+7y+4z=17$
$(3.5)+7(1.5)+4z=17$
$3.5+10.5+4z=17$
$4z=17-14$
$z=0.75$
The solution is $(x=3.5,y=1.5,z=0.75)$
